Lesson 8: Transformations — Reflections & Rotations at the Zoo
Exploring geometric transformations through the lens of zoo design — how enclosure layouts can be reflected and rotated to create efficient, animal-centred spaces.
🎯 Ngā Whāinga Akoranga | Learning Intentions
What a reflection is (flipping across an axis) and how to find reflected coordinates; what a rotation is (turning around a point) and how 90°, 180°, and 270° rotations change (x,y) coordinates.
Reflect four enclosure coordinates across the x-axis and y-axis; rotate a simple enclosure shape 90° and 180° around the origin and record the transformed coordinates.
🎥 Media Anchor & Mathematical Scaffold
Mathematics in Context: Hamilton Zoo
Watch the full clip — 7:22. Source: Khan Academy. The clip teaches the method; the zoo context is ours, and the lesson applies it to real enclosure coordinates.
🧠 1. Before Viewing
If an enclosure is at position (3,4), where would its reflection land if you flipped it across the y-axis? Across the x-axis? Think before we work it out.
👁️ 2. During Viewing
- Early in the clip: Reflection across y-axis: (x,y) becomes (-x,y). Apply this rule to the enclosure at (3,4). Where does it end up?
- Midway: Reflection across x-axis: (x,y) becomes (x,-y). Apply this to (3,4). Where does it land?
- Later in the clip: 90° rotation rule: (x,y) becomes (-y,x). Apply to (3,4). Check: what happens after FOUR 90° rotations? Do you return to the start?
🗣️ 3. After Viewing — Kaiako Move
Kaiako Move: Use a projected coordinate grid with a simple zoo enclosure shape. Model each transformation step by step, checking the rules. Have students predict before you show the answer.
Task: Transformation Zoo: Apply reflection across both axes and 90° rotation to four different enclosure positions. Record the original and transformed coordinates in a table.
⚡ Whakaoho | Do Now (5 mins)
Quick mental transformation: if an enclosure is at (4,2), where is its reflection across the x-axis? Across the y-axis? Write both without drawing first.
📐 Activity 1: Guided Mathematical Exploration (25 mins)
Transformation challenge: design a zoo section that uses 4-fold rotational symmetry. Each enclosure in one quadrant has corresponding enclosures in the other three at rotated coordinates.
✍️ Activity 2: Application & Reflection (20 mins)
Reflection journal: explain in your own words the difference between a reflection and a rotation using two zoo examples. Include the coordinate rules for each.
🏫 Kaiako Planning & Pedagogy Notes
Curriculum Alignment: Te Mātaiaho Mathematics Phase 3/4 — Geometry: understand and apply reflections and rotations on the Cartesian plane.
Hamilton Zoo Context: All tasks use authentic zoo spatial data. Print the map and, if you can, tracing paper — physically rotating a traced enclosure settles arguments fast.
Cultural Connection: Kōwhaiwhai and tukutuku use reflection and rotation with meaning attached to the arrangement, not only to the geometry. Ākonga are analysing transformations here; that analysis is theirs, and it is not a claim about what the pattern tradition intended.